Statistical mechanics of the self-gravitating gas: Thermodynamic limit, instabilities and phase diagrams

International audienceWe show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N,V)-->∞, keeping N/V fixed, that is, with eta≡GmNVT fixed. We develop Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locallyp(r-->)=Trho(r-->), that is a local ideal gas equation of state. The system is in a gaseous phase for etaeta in the CE with the pressure becoming large and negative. The isothermal compressibility diverges at eta=eta. We compute the fluctuations around mean field for the three ensembles. We show that the particle distribution can be described by a Haussdorf dimension